If -2 < a < 11 and 3 < b < 12, then which of the

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

If -2 < a < 11 and 3 < b < 12, then which of the

by swerve » Sat Nov 25, 2017 8:06 am

$$If\ \ -2 < a < 11$$ and $$3 < b < 12$$
Then which of the following is NOT always true?

$$A.\ \ 1 < a + b < 23$$
$$B.\ \ -14 < a - b < 8$$
$$C.\ \ -7 < b - a < 14$$
$$D.\ \ 1 < b + a < 23$$
$$E.\ \ -24 < a*b < 132$$

The OA is C.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Sat Nov 25, 2017 8:06 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Nov 29, 2017 8:35 am

swerve wrote:$$If\ \ -2 < a < 11$$ and $$3 < b < 12$$
Then which of the following is NOT always true?

$$A.\ \ 1 < a + b < 23$$
$$B.\ \ -14 < a - b < 8$$
$$C.\ \ -7 < b - a < 14$$
$$D.\ \ 1 < b + a < 23$$
$$E.\ \ -24 < a*b < 132$$

The OA is C.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

If we can find values for a and b that CONTRADICT one of the answer choices, then that answer choice will be correct.

Answer choice C: -7 < b - a < 14
From the given information, b COULD equal 3.1 and a COULD equal 10. 9
In this case, b - a = 3.1 - 10.9 = -7.8
HOWEVER, answer choice C says that b - a is GREATER than -7 (which it is not)

So, the correct answer must be C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 12, 2019 3:54 pm

swerve wrote:$$If\ \ -2 < a < 11$$ and $$3 < b < 12$$
Then which of the following is NOT always true?

$$A.\ \ 1 < a + b < 23$$
$$B.\ \ -14 < a - b < 8$$
$$C.\ \ -7 < b - a < 14$$
$$D.\ \ 1 < b + a < 23$$
$$E.\ \ -24 < a*b < 132$$

The OA is C.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

The values of (b - a) range from 3 - 11 = -8 to 12 - (-2) = 14. That is, -8 < b - a < 14. Since (b - a) could be, for example, -7.5, we see that the inequality in choice C is not always true.

Answer: C

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